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He preferred our wild, desperate guesses to silence, and he was even more delighted when those guesses led to new problems that took us beyond the original one. He had a special feeling for what he called the “correct miscalculation,” for he believed that mistakes were often as revealing as the right answers. This gave us confidence even when our best efforts came to nothing.
“That’s right! The sum of the factors of 220 is 284, and the sum of the factors of 284 is 220. They’re called ‘amicable numbers,’ and they’re extremely rare.
“The square root sign is a generous symbol, it gives shelter to all the numbers.”
Whether it was a word problem or just a simple calculation, the Professor made Root read it aloud first.
“A problem has a rhythm of its own, just like a piece of music,” the Professor said. “Once you get the rhythm, you get the sense of the problem as a whole, and you can see where the traps might be waiting.”
“For all natural numbers greater than 3, there exist no integers x, y, and z, such that: xn + yn = zn.
I knew what was meant by π. It was a mathematical constant—the ratio of a circle’s circumference to its diameter.
I learned that the logarithm of a given number is the power by which you need to raise a fixed number, called the base, in order to produce the given number. So, for example, if the fixed number, or base, is 10, the logarithm of 100 is 2: 100 = 102 or log10100.
In other words, e is the “base of the natural logarithm.”
If you added 1 to e elevated to the power of π times i, you got 0: eπi + 1 = 0.
On June 24, 1993, there was an article in the newspaper about Andrew Wiles, an Englishman teaching at Princeton University. He had proven Fermat’s Last Theorem.
